Local heritage listing of buildings (and occasionally other kinds of heritage) by local authorities has happened for decades. It is not the same as national statutory listing, but it gives heritage a degree of protection via the planning system (there is a CLA Guidance Note on this, available on the advice pages of the CLA website). After much CLA lobbying Historic England published advice on this in 2012, suggesting that sound procedures are followed including consultation of owners and the community. This consultation was on an updated version of this advice.
Local Heritage Listing: Identifying and conserving local heritage